SOLUTION: how do you write y=-4x^2+8x-1 in vertex form?

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Question 151718: how do you write y=-4x^2+8x-1 in vertex form?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to write y=-4x%5E2%2B8x-1 in vertex form, we need to complete the square.




-4x%5E2%2B8x-1 Start with the right side.


-4%28x%5E2-2x%2B1%2F4%29 Factor out the x%5E2 coefficient -4. This step is very important, the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -2 to get -1. In other words, %281%2F2%29%28-2%29=-1.


Now square -1 to get 1. In other words, %28-1%29%5E2=%28-1%29%28-1%29=1


-4%28x%5E2-2x%2Bhighlight%281-1%29%2B1%2F4%29 Now add and subtract 1 inside the parenthesis. Make sure to place this after the "x" term. Notice how 1-1=0. So the expression is not changed.


-4%28%28x%5E2-2x%2B1%29-1%2B1%2F4%29 Group the first three terms.


-4%28%28x-1%29%5E2-1%2B1%2F4%29 Factor x%5E2-2x%2B1 to get %28x-1%29%5E2.


-4%28%28x-1%29%5E2-3%2F4%29 Combine like terms.


-4%28x-1%29%5E2-4%28-3%2F4%29 Distribute.


-4%28x-1%29%5E2%2B3 Multiply.


So after completing the square, -4x%5E2%2B8x-1 transforms to -4%28x-1%29%5E2%2B3. So -4x%5E2%2B8x-1=-4%28x-1%29%5E2%2B3.




So y=-4x%5E2%2B8x-1 is equivalent to y=-4%28x-1%29%5E2%2B3.


So the expression y=-4%28x-1%29%5E2%2B3 is now in vertex form y=a%28x-h%29%5E2%2Bk where a=-4, h=1 and k=3.